\newproblem{lay:4_3_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.3.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Determine whether the set $B=\{(1,0,0),(1,1,0),(1,1,1)\}$ is a basis or not for $\mathbb{R}^3$. If it is not,
	determine if it is linearly independent.
}{
  % Solution
	$B$ has three linearly independent vectors because if we form the matrix $A=\begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{pmatrix}$
	the unique solution of the equation $A\mathbf{x}=\mathbf{0}$ is $\mathbf{x}=\mathbf{0}$.
	
	Since $B$ has 3 linearly independent vectors, it spans $\mathbb{R}^3$ and it is, therefore, a basis for $\mathbb{R}^3$.
}
\useproblem{lay:4_3_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
